The Third Movie was written
Allan Quatermain and the Jewel of the East
Richard Chamberlain was set to reprise his role as Allan Quatermain. It made it to IMDB
https://www.imdb.com/title/tt2292558/
and this place
https://en.kinorium.com/645621/
Does anyone know if the script was ever released?
This was all I uncovered about the plot.
Drawn out of retirement by the murder of an old friend, Allan Quatermain and his family, aided by an unlikely ally, must travel into the jungles of Central Africa to a legendary lost city to return a diamond stolen from a Chinese museum. But the Chinese and a troop of Nazi war criminal treasure hunters are hot on their trail.